Answer:
30
Step-by-step explanation:
Given the information that points [tex] \sf B[/tex], [tex] \sf D[/tex], and [tex] \sf F[/tex] are midpoints of the sides of triangle [tex] \sf ACE[/tex], we can use the mid-segment theorem which states that the length of the segment joining the midpoints of two sides of a triangle is half the length of the third side.
Given:
- [tex] \sf EC = 44[/tex]
- [tex] \sf DF = 15[/tex]
According to the mid-segment theorem:
- [tex] \sf BF = \dfrac{1}{2}CE[/tex]
- [tex] \sf BD = \dfrac{1}{2}AC[/tex]
- [tex] \sf DF = \dfrac{1}{2}AC[/tex]
We are given that [tex] \sf DF = 15[/tex], which means:
[tex] \sf DF = \dfrac{1}{2}AC [/tex]
Substitute value of DF.
[tex] 15 = \dfrac{1}{2}AC [/tex]
Multiply both sides by 2.
[tex] \sf 2 \times 15 = AC [/tex]
[tex]\sf 30 = AC [/tex]
Therefore, [tex] \sf AC = 30[/tex].
